Related papers: The Difference Kapranov Theorem

We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As…

A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.

Even though flt is a number theoretic result we prove that the result depends on the topological as well as the field structure of the underlying space.

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…

We provide sufficient conditions for the existence of a global diffeomorphism between tame Fr\'{e}chet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient in the proof of the main theorem.

Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude…

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…

We develop a geometric theory for difference equations with a given group of automorphisms. To solve this problem we extend the class of difference fields to the class of absolutely flat simple difference rings called pseudofields. We prove…

This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in the second…

The main result of this work is a new proof and generalization of Lazard's comparison theorem of locally analytic group cohomology with Lie algebra cohomology for K-Lie groups, where K is a finite extension of the p-adic numbers. We show…

We recall the well-known Chern-Terng theorem concerning affine minimal surfaces. Next we formulate some complementary (with transversal fields necessarily not parallel) affine B\"acklund theorem. We describe some geometrical conditions…

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…

Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi…

Understanding the algebraic structure underlying a manifold with a general affine connection is a natural problem. In this context, A. V. Gavrilov introduced the notion of framed Lie algebra, consisting of a Lie bracket (the usual Jacobi…

This, and its sequel, concern some variations of a classical theorem of A.D. Alexandrov and teh Hopf Lemma.

We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand-Kapranov-Zelevinsky into various directions.

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…

In this article we analyze the global diffeomorphism property of polynomial maps $F:\mathbb{R}^n\rightarrow\mathbb{R}^n$ by studying the properties of the Newton polytopes at infinity corresponding to the sum of squares polynomials…

The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…

We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.